Journal
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
Volume 53, Issue 1, Pages 155-171Publisher
SPRINGER
DOI: 10.1007/s10589-011-9444-9
Keywords
Optimal control; Optimal actuator placement; Non-reflexive Banach space; Radon measures; Fenchel duality
Funding
- Austrian Science Fund (FWF) [SFB F32]
- Austrian Science Fund (FWF) [W1244] Funding Source: Austrian Science Fund (FWF)
- Austrian Science Fund (FWF) [F 3202] Funding Source: researchfish
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The problem of optimal placement of point sources is formulated as a distributed optimal control problem with sparsity constraints. For practical relevance, partial observations as well as partial and non-negative controls need to be considered. Although well-posedness of this problem requires a non-reflexive Banach space setting, a primal-predual formulation of the optimality system can be approximated well by a family of semi-smooth equations, which can be solved by a superlinearly convergent semi-smooth Newton method. Numerical examples indicate the feasibility for optimal light source placement problems in diffusive photochemotherapy.
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